A color image edge detection algorithm is proposed in
this paper using Pseudo-complement and matrix rotation operations.
First, pseudo-complement method is applied on the image for each
channel. Then, matrix operations are applied on the output image of
the first stage. Dominant pixels are obtained by image differencing
between the pseudo-complement image and the matrix operated
image. Median filtering is carried out to smoothen the image thereby
removing the isolated pixels. Finally, the dominant or core pixels
occurring in at least two channels are selected. On plotting the
selected edge pixels, the final edge map of the given color image is
obtained. The algorithm is also tested in HSV and YCbCr color
spaces. Experimental results on both synthetic and real world images
show that the accuracy of the proposed method is comparable to
other color edge detectors. All the proposed procedures can be
applied to any image domain and runs in polynomial time.

Phylogenetic tree is a graphical representation of the
evolutionary relationship among three or more genes or organisms.
These trees show relatedness of data sets, species or genes
divergence time and nature of their common ancestors. Quality of a
phylogenetic tree requires parsimony criterion. Various approaches
have been proposed for constructing most parsimonious trees. This
paper is concerned about calculating and optimizing the changes of
state that are needed called Small Parsimony Algorithms. This paper
has proposed enhanced small parsimony algorithm to give better
score based on number of evolutionary changes needed to produce
the observed sequence changes tree and also give the ancestor of the
given input.

In practice, wireless networks has the property that
the signal strength attenuates with respect to the distance from the
base station, it could be better if the nodes at two hop away are
considered for better quality of service. In this paper, we propose a
procedure to identify delay preserving substructures for a given
wireless ad-hoc network using a new graph operation G 2 – E (G) =
G* (Edge difference of square graph of a given graph and the
original graph). This operation helps to analyze some induced
substructures, which preserve delay in communication among them.
This operation G* on a given graph will induce a graph, in which 1-
hop neighbors of any node are at 2-hop distance in the original
network. In this paper, we also identify some delay preserving
substructures in G*, which are (i) set of all nodes, which are mutually
at 2-hop distance in G that will form a clique in G*, (ii) set of nodes
which forms an odd cycle C2k+1 in G, will form an odd cycle in G*
and the set of nodes which form a even cycle C2k in G that will form
two disjoint companion cycles ( of same parity odd/even) of length k
in G*, (iii) every path of length 2k+1 or 2k in G will induce two
disjoint paths of length k in G*, and (iv) set of nodes in G*, which
induces a maximal connected sub graph with radius 1 (which
identifies a substructure with radius equal 2 and diameter at most 4 in
G). The above delay preserving sub structures will behave as good
clusters in the original network.

In this paper, estimation of the linear regression
model is made by ordinary least squares method and the
partially linear regression model is estimated by penalized
least squares method using smoothing spline. Then, it is
investigated that differences and similarity in the sum of
squares related for linear regression and partial linear
regression models (semi-parametric regression models). It is
denoted that the sum of squares in linear regression is reduced
to sum of squares in partial linear regression models.
Furthermore, we indicated that various sums of squares in the
linear regression are similar to different deviance statements in
partial linear regression. In addition to, coefficient of the
determination derived in linear regression model is easily
generalized to coefficient of the determination of the partial
linear regression model. For this aim, it is made two different
applications. A simulated and a real data set are considered to
prove the claim mentioned here. In this way, this study is
supported with a simulation and a real data example.

One of the purposes of the robust method of
estimation is to reduce the influence of outliers in the data, on the
estimates. The outliers arise from gross errors or contamination from
distributions with long tails. The trimmed mean is a robust estimate.
This means that it is not sensitive to violation of distributional
assumptions of the data. It is called an adaptive estimate when the
trimming proportion is determined from the data rather than being
fixed a “priori-.
The main objective of this study is to find out the robustness
properties of the adaptive trimmed means in terms of efficiency, high
breakdown point and influence function. Specifically, it seeks to find
out the magnitude of the trimming proportion of the adaptive
trimmed mean which will yield efficient and robust estimates of the
parameter for data which follow a modified Weibull distribution with
parameter λ = 1/2 , where the trimming proportion is determined by a
ratio of two trimmed means defined as the tail length. Secondly, the
asymptotic properties of the tail length and the trimmed means are
also investigated. Finally, a comparison is made on the efficiency of
the adaptive trimmed means in terms of the standard deviation for the
trimming proportions and when these were fixed a “priori".
The asymptotic tail lengths defined as the ratio of two trimmed
means and the asymptotic variances were computed by using the
formulas derived. While the values of the standard deviations for the
derived tail lengths for data of size 40 simulated from a Weibull
distribution were computed for 100 iterations using a computer
program written in Pascal language.
The findings of the study revealed that the tail lengths of the
Weibull distribution increase in magnitudes as the trimming
proportions increase, the measure of the tail length and the adaptive
trimmed mean are asymptotically independent as the number of
observations n becomes very large or approaching infinity, the tail
length is asymptotically distributed as the ratio of two independent
normal random variables, and the asymptotic variances decrease as
the trimming proportions increase. The simulation study revealed
empirically that the standard error of the adaptive trimmed mean
using the ratio of tail lengths is relatively smaller for different values
of trimming proportions than its counterpart when the trimming
proportions were fixed a 'priori'.

This paper studies the effect of different compression
constraints and schemes presented in a new and flexible paradigm to
achieve high compression ratios and acceptable signal to noise ratios
of Arabic speech signals. Compression parameters are computed for
variable frame sizes of a level 5 to 7 Discrete Wavelet Transform
(DWT) representation of the signals for different analyzing mother
wavelet functions. Results are obtained and compared for Global
threshold and level dependent threshold techniques. The results
obtained also include comparisons with Signal to Noise Ratios, Peak
Signal to Noise Ratios and Normalized Root Mean Square Error.

In this paper, we define permutable and mutually permutable fuzzy subgroups of a group. Then we study their relation with permutable and mutually permutable subgroups of a group. Also we study some properties of fuzzy quasinormal subgroup. We define superfuzzy subset of a fuzzy subset and we study some properties of superfuzzy subset of a fuzzy subset.